Environmental Modeling & Assessment

, Volume 18, Issue 3, pp 259–270 | Cite as

Some Dependence Models for the Time Between Ozone Exceedances in Mexico City

  • Jorge A. Achcar
  • Eliane R. Rodrigues
  • Edilberto Cepeda-Cuervo


In this paper, we consider several modelling approaches for the mean time between exceedances of a given environmental threshold. The interest here resides in the time between ozone exceedances (also called ozone inter-exceedances times). The proposed models assume two basic density functions for the time between surpassings: the Weibull and the generalised exponential functions. Considering those distributions, a random effect with autoregressive structure is taken into account to determine unexpected changes in the mean of the inter-exceedances density functions. Those unexpected changes could be captured either by their scale parameter or by both their scale and shape parameters. The models are applied to ozone data from the monitoring network of Mexico City. Selection of the model that best explains the data is performed using the deviance information criterion and also the sum of the absolute values of the differences between the estimated and observed means of the inter-exceedances times. An analysis to detect the possible presence of change-points is also presented.


MCMC algorithms Bayesian inference Dependence models Inter-exceedances times Change-points Ozone air pollution Mexico city 



We thank an anonymous reviewer and the editor in chief for the constructive comments and suggestions that helped to improve the presentation of this work. The authors thank Guadalupe Tzintzun from the Instituto Nacional de Ecología of the Secretaría de Medio Ambiente y Recursos Naturales, Mexico, for providing the ozone data. ERR received financial support from the project PAPIIT-IN104110-3 of the Dirección General de Apoyo al Personal Académico of the Universidad Nacional Autónoma de México, Mexico. JAA was partially supported by the grant number 300235/2005-4 of the Conselho Nacional de Pesquisa, Brazil.


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Jorge A. Achcar
    • 1
  • Eliane R. Rodrigues
    • 2
  • Edilberto Cepeda-Cuervo
    • 3
  1. 1.Departamento de Medicina Social, Faculdade de Medicina de Ribeirão PretoUSPRibeirão PretoBrazil
  2. 2.Instituto de MatemáticasUniversidad Nacional Autónoma de MéxicoMexico CityMexico
  3. 3.Departamento de EstadísticaUniversidad Nacional de ColombiaBogotáColombia

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